# A retroanalysis problem in bridge

This is an entry into the 29th fortnightly topic challenge - Retrograde Analysis.

You're passing a bridge table when one of the players (South) is called away suddenly. He gives you his hand and says "There are no trumps. You need all seven tricks. It's your lead." before disappearing. You find that you're declarer, South, with these hands:

    ♠ K2
♡ Q2
♢ 2
♣ 32

N
W       E
S

♠ A3
♡ AJ
♢ A3
♣ A


The other players refuse to tell you anything about the play of the first six tricks. You lead your aces, and both defenders follow suit.

How do you play the last three tricks?

This problem is a variation, by me, of one by Jonathan Mestel.

• Thanks for participating in the challenge, we need a few more seeing as this is only the second Apr 1, 2017 at 7:49

6 rounds have been played and no-one has any voids before you sit down. There are therefore at most 1 round of spades and hearts (if there were 2 then 8 cards are played + 4 visible + 2 with the opponents =14), and 2 rounds of diamonds and clubs.

The only way to get to 6 is if exactly those were played, meaning that before you sat down there had been 1 round of spades and hearts and 2 of diamonds and clubs.

Of course, you had no way of knowing that until you played your aces, which was therefore grotesquely irresponsible, but we will leave that aside for now.

The point is that your opponents are now void in diamonds and clubs. We assume the King of hearts is still out.

So:

3D (discarding the QH); 3S to KS; 3C (discarding the JH)

• Yes, cashing all 4 aces before thinking was perhaps unwise (who knows, before thinking, whether or not you'd better make the lead pass from S to N and back to S). But then I think that is a defect of Mestel's original, where there's 5 tricks to play, and again S cashes all 4 aces first. Apr 4, 2017 at 14:30
• My comment was tongue in cheek. It's a great puzzle. It seems there are fewer bridge players than you might expect in such a forum, because I think it deserves more than the current 7 that you've got! It might have been possible to know that this was the best way to play. If you were keeping tabs from the beginning you might play the aces, but I think a finesse in hearts might be better. So 3 to the KS, and then QH, covering the K if East plays it and otherwise playing the 2 and hoping for the best Apr 4, 2017 at 20:33